1. Field of the Invention
This invention relates to receivers of electromagnetic signals employing multicarrier modulation. More particularly this invention relates to synchronization of a timed interval which is required for the calculation of a fast Fourier transform in a receiver employing orthogonal frequency division multiplexing.
2. Description of the Related Art
Coded orthogonal frequency division multiplexing ("COFDM") has been proposed for digital audio and digital video broadcasting, both of which require efficient use of limited bandwidth, and a method of transmission which is reliable in the face of several effects. For example the impulse response of a typical channel can be modeled as the sum of a plurality of Dirac pulses having different delays. Each pulse is subject to a multiplication factor, in which the amplitude generally follows a Rayleigh law. Such a pulse train can extend over several microseconds, making unencoded transmission at high bit rates unreliable. In addition to random noise, impulse noise, and fading, other major difficulties in digital terrestrial transmissions at high data rates include multipath propagation, and adjacent channel interference, where the nearby frequencies have highly correlated signal variations. COFDM is particularly suitable for these applications. In practical COFDM arrangements, relatively small amounts of data are modulated onto each of a large number of carriers that are closely spaced in frequency. The duration of a data symbol is increased in the same ratio as the number of carriers or subchannels, so that inter-symbol interference is markedly reduced.
Multiplexing according to COFDM is illustrated in FIGS. 1 and 2, wherein the spectrum of a single COFDM carrier or subchannel is indicated by line 2. A set of carrier frequencies is indicated by the superimposed waveforms in FIG. 2, where orthogonality conditions are satisfied. In general two real-valued functions are orthogonal if ##EQU1## where K is a constant, and K=0 if p.noteq.q; K.noteq.0 if p=q. Practical encoding and decoding of signals according to COFDM relies heavily on the fast Fourier transform ("FFT"), as can be appreciated from the following equations.
The signal of a carrier c is given by EQU s.sub.c (t)=A.sub.c (t)e.sup.j.omega..sbsp.c.sup.+.phi..sbsp.c.sup.(t)!( 2 )
where A.sub.c is the data at time t, .omega..sub.c is the frequency of the carrier, and .phi..sub.c is the phase. N carriers in the COFDM signal is given by ##EQU2## Sampling over one symbol period, then EQU .phi..sub.c (t)=&gt;.phi..sub.n ( 5) EQU A.sub.c (t)=&gt;A.sub.n ( 6)
With a sampling frequency of 1/T, the resulting signal is represented by ##EQU3## Sampling over the period of one data symbol T=NT, with .omega..sub.0 =0, ##EQU4## which compares with the general form of the inverse discrete Fourier transform: ##EQU5## In the above equations A.sub.n e.sup.j.phi..sub.n is the input signal in the sampled frequency domain, and s.sub.s (kT) is the time domain representation. It is known that increasing the size of the FFT provides longer symbol durations and improves ruggedness of the system as regards echoes which exceed the length of the guard interval. However computational complexity increases according to Nlog.sub.2 N, and is a practical limitation.
In the presence of intersymbol interference caused by the transmission channel, orthogonality between the signals is not maintained. One approach to this problem has been to deliberately sacrifice some of the emitted energy by preceding each symbol in the time domain by an interval which exceeds the memory of the channel, and any multipath delay. The "guard interval" so chosen is large enough to absorb any intersymbol interference, and is established by preceding each symbol by a replication of a portion of itself. The replication is typically a cyclic extension of the terminal portion of the symbol. Referring to FIG. 3, a data symbol 4 has an active interval 6 which contains all the data transmitted in the symbol. The terminal portion 8 of the active interval 6 is repeated at the beginning of the symbol as the guard interval 10. The COFDM signal is represented by the solid line 12. It is possible to cyclically repeat the initial portion of the active interval 6 at the end of the symbol.
Transmission of COFDM data can be accomplished according to the known general scheme shown in FIG. 4. A serial data stream 14 is converted to a series of parallel streams 16 in a serial-to-parallel converter 18. Each of the parallel streams 16 is grouped into x bits each to form a complex number, where x determines the signal constellation of its associated parallel stream. After outer coding and interleaving in block 20 pilot carriers are inserted via a signal mapper 22 for use in synchronization and channel estimation in the receiver. The pilot carriers are typically of two types. Continual pilot carriers are transmitted in the same location in each symbol, with the same phase and amplitude. In the receiver, these are utilized for phase noise cancellation, automatic frequency control, and time/sampling synchronization. Scattered pilot carriers are distributed throughout the symbol, and their location typically changes from symbol to symbol. They are primarily useful in channel estimation. Next the complex numbers are modulated at baseband by the inverse fast fourier transform ("IFFT") in block 24. A guard interval is then inserted at block 26. The discrete symbols are then converted to analog, typically low-pass filtered, and then upconverted to radiofrequency in block 28. The signal is then transmitted through a channel 30 and received in a receiver 32. As is well known in the art, the receiver applies an inverse of the transmission process to obtain the transmitted information. In particular an FFT is applied to demodulate the signal.
A modern application of COFDM has been proposed in the European Telecommunications Standard DRAFT pr ETS 300 744 (May 1996), which specifies the framing structure, channel coding, and modulation for digital terrestrial television. The specification was designed to accommodate digital terrestrial television within the existing spectrum allocation for analog transmissions, yet provide adequate protection against high levels of co-channel interference and adjacent channel interference. A flexible guard interval is specified, so that the system can support diverse network configurations, while maintaining high spectral efficiency, and sufficient protection against co-channel interference and adjacent channel interference from existing PAL/SECAM services. The noted European Telecommunications Standard defines two modes of operation. A "2K mode", suitable for single transmitter operation and for small single frequency networks with limited transmitter distances. An "8K mode" can be used for either single transmitter operation or for large single frequency networks. Various levels of quadrature amplitude modulation ("QAM") are supported, as are different inner code rates, in order to balance bit rate against ruggedness. The system is intended to accommodate a transport layer according to the Moving Picture Experts Group ("MPEG"), and is directly compatible with MPEG-2 coded TV signals (ISO/IEC 13818).
In the noted European Telecommunications Standard data carriers in a COFDM frame can be either quadrature phase shift keyed ("QPSK"), 16-QAM, 64-QAM, non-uniform 16-QAM, or non-uniform 64-QAM using Gray mapping.
An important problem in the reception of COFDM transmission is difficulty in maintaining synchronization due to phase noise and jitter which arise from upconversion prior to transmission, downconversion in the receiver, and the front end oscillator in the tuner, which is typically a voltage controlled oscillator. Except for provision of pilot carriers to aid in synchronization during demodulation, these issues are not specifically addressed in the noted European Telecommunications Standard, but are left for the implementer to solve.
Basically phase disturbances are of two types. First, noisy components which disturb neighbor carriers in a multicarrier system are called the "foreign noise contribution" ("FNC"). Second, a noisy component which disturbs its own carrier is referred to as the "own noise contribution".
Referring to FIG. 5, the position of ideal constellation samples are indicated by "x" symbols 34. The effect of foreign noise contribution is stochastic, resulting in Gaussian-like noise. Samples perturbed in this manner are indicated on FIG. 5 as circles 36. The effects of the own noise contribution is a common rotation of all constellation points, indicated as a displacement between each "x" symbol 34 and its associated circle 36. This is referred to as the "common phase error", which notably changes from symbol to symbol, and must therefore be recalculated each symbol period T.sub.s. The common phase error may also be interpreted as a mean phase deviation during the symbol period T.sub.s.
In order for the receiver 32 to process the data symbols in a practical system, a mathematical operation is performed on the complex signal representing each data symbol. Generally this is an FFT. For valid results to be obtained, a particular form of timing synchronization is required in order to align the FFT interval with the received data symbol.